
where
\(\mathbf {A}_{\mathrm {R}}\! =\! \left[\varphi _{N_1}(\nu _1),\cdots ,\varphi _{N_1}(\nu _{{N_1}^{^{\prime }}})\right]\!\otimes \! \left[\varphi _{N_2}(\varsigma _1),\cdots ,\varphi _{N_2}(\varsigma _{{N_2}^{^{\prime }}})\right]\in \mathbb {C}^{N \times N_1^{\prime } N_2^{\prime }}\) ,
and \(\lambda _k\in \mathbb {C}^{N_1^{\prime } N_2^{\prime }}\)  represents the channel coefficients of \(\mathbf {h}_k\)  in the angular domain. Since the number of paths is usually limited, \(\lambda _k \)  is essentially sparse, with each nonzero value being the corresponding composite path gain \(\sqrt{\mu _k}\epsilon _i^k\) . The exploitation of such a sparse structure has been shown to bring improved channel estimation performance and reduced complexity [1]}, [2]}, [3]}, [4]}.
